Short AnswerThere are two numbers
x1 = -0.25 + 0.9682i <<<<
answer 1x2 = - 0.25 - 0.9582i <<<<
answer 2 I take it there are two such numbers.
Let one number = x
Let one number = y
x + y = -0.5
y = - 0.5 - x (1)
xy = 1 (2)
Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1 Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0 Order these by powers
-x^2 - 0.5x -1 = 0 Multiply though by - 1
x^2 + 0.5x + 1 = 0 Use the quadratic formula to solve this.

a = 1
b = 0.5
c = 1

x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i
x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i
These two are conjugates. They will add as x1 + x2 = -0.25 - 0.25 = - 0.50.
The complex parts cancel out. Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.
Check(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375
NoticeThe two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.
The final result is 0.9375 and 0.0625 add up to 1
Answer:
Hence he will be 4 large containers and 4 small containers
Step-by-step explanation:
Given data
Let the number of small containers be x
and the number of large containers be y
x+y= 8---------1
also
2x+4y= 24-----2
the system of equation to solve the problem is
x+y= 8
2x+4y= 24
from 1
x=8-y
put this in 2
2(8-y)+4y= 24
16-2y+4y= 24
2y= 24-16
2y= 8
y= 8/2
y= 4
put y= 4 in 1
x+4=8
x= 8-4
x= 4
Hence he will be 4 large containers and 4 small containers
Given:
Length = x + x + 3 = 2x + 3
Width = 2 + x
Area = length * width
91 ft² = (2x + 3) (2+x)
91 = 4x + 2x² + 6 + 3x
0 = 2x² + 7x + 6 - 91
0 = 2x² + 7x - 85
(2x + 17) ( x - 5)
x = -17/2 or x = 5
Let x = 5 ;
length = 2x + 3 = 2(5) + 3 = 13
width = 2 + x = 2 + 5 = 7
Area = 13 x 7 = 91
Perimeter = 2(length + width)
Perimeter = 2(13 + 7)
Perimeter = 2(20)
Perimeter = 20 feet of fencing